Nexus 5 International Usage Questions

I have a couple questions concerning international usage for my Nexus 5. I'm currently using it for Sprint in the US. I believe that it is the phone from Sprint. I'm not sure because I bought it second hand. The previous owner didn't tell me where it's from.

But currently, I'm using it on Sprint LTE data services.

I'm going to Canada for 2 months in July and I'd like to use my Nexus 5 on either Rogers(preferred) or Bell.

Id like to use Rogers or Bell's LTE service, but from what I hear is that the US version of the phone only allows US carrier LTE service and only 3G international service.

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